U.S. patent application entitled xe2x80x9cMinimum Mean-Squared Error Block-Decision Feedback Sequence Estimation in Digital Communication Systemsxe2x80x9d by Ratnarajah et al., filed on same date, and assigned to the assignee of the present application, discloses and claims subject matter related to that of the present invention and is herein incorporated by reference.
This invention relates to digital communication systems, and more particularly to the estimation of the sequence of transmitted symbols in such systems.
In EDGE (Enhanced Data Rates for GSM Evolution) cellular communication systems a sequence of symbols is transmitted as an 8 Phase Shift Keying (8-PSK) modulated signal. The signal may propagate along several propagation paths to a receiver. If the time delay between the various propagation paths is comparable to the intersymbol period, then the""signal received by the receiver will contain intersymbol interference. The attenuation along each path will vary, as will phase changes due to reflections, so the intersymbol interference will not be merely additive. In addition, transmitted symbols in neighbouring cells in Time Division Multiple Access systems can cause co-channel interference. Finally, the received signal will contain noise, which is assumed to be additive white Gaussian noise.
The receiver must estimate the transmitted sequence of symbols s from the received sequence of signal samples x. In a diversity receiver having M antennae, the M spatially distinct received signal samples at any discrete time k can be represented as a vector Xk=[x1, . . . , xM]kT. A hybrid receiver considers the contributions of co-channel interference and intersymbol interference separately. The hybrid receiver includes a space-time filter which acts on the M received signal samples xk to mitigate co-channel interference, and an equalizer which then corrects for intersymbol interference. The output of the equalizer is an estimated sequence of symbols ŝ which ideally is equal to the transmitted sequence of symbols s.
If the space-time filter takes L+1 delayed time-taps of the received signal, then the spatially distinct received signal samples xk can be extended to include temporal distinctions. If ordered sequentially, the received signal samples can be represented as a space-time stacked vector of vectors xk=[xkT, . . . , xkxe2x88x92LT]T of length M(L+1), or             x      _        k    =      [                                        x                          1              ,              k                                                            ⋮                                                  x                          M              ,              k                                                                        x                          1              ,                              k                -                1                                                                          ⋮                                                  x                          M              ,                              k                -                1                                                                          ⋮                                                  x                          1              ,                              k                -                L                                                                          ⋮                                                  x                          M              ,                              k                -                L                                                          ]  
where for each element of the vector the first subscript refers to the antenna at which the signal sample was received, and the second subscript refers to the time-tap.
An intermediate signal sample yk can be defined as an output of the space-time filter such that yk=wTxk where w is a vector of M(L+1). space-time filter coefficients, w=[w1, 1, . . . , wM,1, . . . , w1,L+1, . . . , wM,L+1]T. For a sequence of N received signal samples, the space-time stacked vector xk is extended to form a matrix X=[xk, . . . , xk+Nxe2x88x921], or   X  =            [                                                  x                              1                ,                k                                                                        x                              1                ,                                  k                  +                  1                                                                          ⋯                                              x                              1                ,                                  k                  +                  N                  -                  1                                                                                          ⋮                                ⋮                                ⋯                                ⋮                                                              x                              M                ,                k                                                                        x                              M                ,                                  k                  +                  1                                                                          …                                              x                              M                ,                                  k                  +                  N                  -                  1                                                                                                        x                              1                ,                                  k                  -                  1                                                                                        x                              1                ,                k                                                          …                                              x                              1                ,                                  k                  +                  N                  -                  2                                                                                          ⋮                                ⋮                                …                                ⋮                                                              x                              M                ,                                  k                  -                  1                                                                                        x                              M                ,                k                                                          …                                              x                              M                ,                                  k                  +                  N                  -                  2                                                                                          ⋮                                ⋮                                …                                ⋮                                                              x                              1                ,                                  k                  -                  L                                                                                        x                              1                ,                                  k                  +                  1                  -                  L                                                                          …                                              x                              1                ,                                  k                  +                  N                  -                  1                  -                  L                                                                                          ⋮                                ⋮                                …                                ⋮                                                              x                              M                ,                                  k                  -                  L                                                                                        x                              M                ,                                  k                  +                  1                  -                  L                                                                          …                                              x                              M                ,                                  k                  +                  N                  -                  1                  -                  L                                                                        ]        ∈          C              M        ⁢                  xe2x80x83                ⁢                  (                      L            +            1                    )                xc3x97        N            
and an intermediate sequence of singal samples y of length N is then produced by the space-time filter such that yTwTX.
The intermediate sequence of signal samples y can also be expressed as yT=hTS+eT where h is a vector of effective channel coefficients, S is a matrix of transmitted symbols of the form       S    =                  [                                                            s                k                                                                    s                                  k                  +                  1                                                                    …                                                      s                                  k                  +                  N                  -                  1                                                                                                        s                                  k                  -                  1                                                                                    s                k                                                    …                                      ⋮                                                          ⋮                                      ⋮                                      ⋰                                      ⋮                                                                          s                                  k                  -                  v                  -                  L                                                                    …                                      …                                                      s                                  k                  -                  v                  -                  L                  +                  N                  -                  1                                                                    ]            ∈              C                              xe2x80x83                    ⁢                                    (                              v                +                L                +                1                            )                        xc3x97            N                                ,
v+1 is the number of propagation paths being considered for the environment in which the signal propagates, v+L+1 is the number of effective channels which will be considered by the equalizer, and e is a disturbance. The effective channel coefficients are used in the equalizer, as discussed below. From the perspective of the equalizer y is a received sequence of signal samples having passed through v+L+1 effective channels with impulse response coefficients given by h, the effective channels consisting of the propagation paths and the effects of the space-time filter.
Combining the two expressions for y, it is seen that the disturbance can be expressed as eT=wTXxe2x88x92hTS. A signal-to-interference-plus-noise ratio SINR can be defined as       SINR    =                            "LeftDoubleBracketingBar"                                                    h                _                            T                        ⁢                          xe2x80x83                        ⁢            S                    "RightDoubleBracketingBar"                2                              "LeftDoubleBracketingBar"                      e            _                    "RightDoubleBracketingBar"                2                  SINR    =                            "LeftDoubleBracketingBar"                                                    h                _                            T                        ⁢                          xe2x80x83                        ⁢            S                    "RightDoubleBracketingBar"                2                              "LeftDoubleBracketingBar"                                                                      w                  _                                T                            ⁢                              xe2x80x83                            ⁢              X                        -                                                            h                  _                                T                            ⁢                              xe2x80x83                            ⁢              S                                "RightDoubleBracketingBar"                2            
The filter coefficients w and the effective channel coefficients h are jointly optimized by maximizing the SINR with respect to w and h to produce optimal coefficients wopt and hopt. Using the technique of separation of variables, hopt is found to be             h      _        opt    =            arg      ⁢              xe2x80x83            ⁢                        max                      h            _                          ⁢                  xe2x80x83                ⁢                                                            h                _                            H                        ⁢                          xe2x80x83                        ⁢                          S              *                        ⁢                          xe2x80x83                        ⁢                          S              T                        ⁢                          xe2x80x83                        ⁢                          h              _                                                                          h                _                            H                        ⁢                          xe2x80x83                        ⁢                          S              *                        ⁢                          xe2x80x83                        ⁢                          P              *                        ⁢                          S              T                        ⁢                          xe2x80x83                        ⁢                          h              _                                            ∈          C                        (                      v            +            L            +            1                    )                xc3x97        1            
where P=(Ixe2x88x92XH(XXH)xe2x88x921X), I is an identity matrix, the superscript H indicates the Hermitian of the matrix or vector to which it refers, and the superscript indicates the complex conjugate of the matrix or vector to which it refers. This is a generalized eigenvalue problem, and hopt is the eigenvector corresponding to the largest eigenvalue of (S*P*ST)xe2x88x921S*ST. wopt is then found from
woptT=hoptTSXH(XXH)xe2x88x921
hopt and wopt can be found if the matrices S and X are formed from known training data. Unfortunately the eigenvalue problem is a complex one, and an efficient method of determining hopt is needed.
Once wopt and hopt are determined the estimated sequence of symbols ŝ can be determined. The intermediate sequence of signal samples y produced by the space-time filter is found from yT=wTX where X is now the matrix of received sequences of signal samples for user data rather than for training data, having N+v+L columns where N is the number of symbols in the transmitted sequence (which is half a slot in EDGE systems). From the perspective of the equalizer, y=Hs+e where H is a matrix of effective channel coefficients having the form   H  =            [                                                  h              1                                                          h              0                                            0                                …                                …                                …                                0                                                              h              2                                                          h              1                                                          h              0                                            ⋯                                ⋯                                ⋯                                0                                                              h              3                                                          h              2                                                          h              1                                            ⋯                                …                                …                                0                                                ⋮                                ⋮                                ⋮                                ⋰                                ⋰                                ⋰                                ⋮                                                              h                              v                +                L                                                                        h                              v                +                L                -                1                                                                        h                              v                +                L                -                2                                                          …                                …                                …                                0                                                0                                              h                              v                +                L                                                                        h                              v                +                L                -                1                                                          …                                …                                …                                0                                                ⋮                                ⋮                                ⋮                                …                                …                                …                                ⋮                              ]        ∈          C                        (                      N            +            v            +            L                    )                xc3x97        N            
and the values of the matrix elements hi are given by hopt, determined earlier during the joint optimization.
One method of estimating the transmitted sequence of symbols in the presence of intersymbol interference is the Maximum Likelihood Sequence Estimation (MLSE) method. For each of the possible transmitted symbols, the received signal is compared with the signal that should have been received if it was that symbol that had been transmitted. Based on these comparisons, the MLSE method then selects the symbol which was most likely to have been transmitted. The MLSE method is a very accurate sequence estimation method. However, the complexity of the MLSE method is proportional to the number of possible transmitted symbols raised to the power of the number of effective channels being considered. In EDGE systems there are eight possible transmitted symbols and seven effective paths are considered (v=5, L=1), and the complexity of the MLSE method makes it impractical.
A second method of estimating the transmitted symbols is the Zero-Forcing Block Linear Equalizer (ZF-BLE) method. In the ZF-BLE method, the quantity Q is minimized with respect to s, where
Q=∥yxe2x88x92Hs∥Ree2,
Ree=xcex5{eeH} is the expectation value of the covariance matrix of the disturbance, and the operator xcex5 denotes an expectation value. The solution to this minimization is
ŝ=(HHReexe2x88x921H)xe2x88x921HHReexe2x88x921y
where ŝ is the estimation of the sequence of transmitted symbols s. However the ZF-BLE method is less than optimum.
A hybrid receiver is needed in which the optimization of the coefficients wopt and hopt is simplified, and in which the sequence estimation method used in the equalizer does not have the complexity of the MLSE method and which improves performance over the ZF-BLE method.
The present invention provides a diversity hybrid receiver in a digital communication system. The receiver includes a joint optimization processor which contains instructions for producing optimal filter coefficients and optimal effective channel coefficients hopt from sequences of received training signal samples and a sequence of known training symbols. The receiver also includes a space-time filter which contains means for producing an intermediate sequence of signal samples y from a received sequence of signal samples and the optimal filter coefficients. The receiver also includes an equalization processor which contains instructions for producing an estimated sequence of symbols ŝ. These instructions comprise: forming a matrix of optimal effective channel coefficients H from the optimal effective channel coefficients hopt; determining a lower triangular matrix L from a relationship LLH=HHReexe2x88x921H+I where LH is the Hermitian of L, HH is the Hermitian of H, I is an identity matrix, and Reeis a covariance matrix of a disturbance e; calculating a vector z=Lxe2x88x921HHReexe2x88x921y; and determining an estimated sequence of symbols ŝ belonging to a set of discrete possible symbol values such that the square of the magnitude of a difference vector LHŝxe2x88x92z is minimized.
A diversity hybrid receiver is also provided in which, either with or without the equalization processor described above, there are M antennae, each antenna receiving one sequence of received training signal samples, and L time-taps of each sequence of received training signal samples is produced. The instructions contained in the joint optimization processor comprise: defining a matrix X from the sequences of received training signal samples as   X  =            [                                                  x                              1                ,                k                                                                        x                              1                ,                                  k                  +                  1                                                                          ⋯                                              x                              1                ,                                  k                  +                  p                                                                                          ⋮                                ⋮                                ⋯                                ⋮                                                              x                              M                ,                k                                                                        x                              M                ,                                  k                  +                  1                                                                          …                                              x                              M                ,                                  k                  +                  p                                                                                                        x                              1                ,                                  k                  -                  1                                                                                        x                              1                ,                k                                                          …                                              x                              1                ,                                  k                  +                  p                  -                  1                                                                                          ⋮                                ⋮                                …                                ⋮                                                              x                              M                ,                                  k                  -                  1                                                                                        x                              M                ,                k                                                          …                                              x                              M                ,                                  k                  +                  p                  -                  1                                                                                          ⋮                                ⋮                                …                                ⋮                                                              x                              1                ,                                  k                  -                  L                                                                                        x                              1                ,                                  k                  +                  1                  -                  L                                                                          …                                              x                              1                ,                                  k                  +                  p                  -                  L                                                                                          ⋮                                ⋮                                …                                ⋮                                                              x                              M                ,                                  k                  -                  L                                                                                        x                              M                ,                                  k                  +                  1                  -                  L                                                                          …                                              x                              M                ,                                  k                  +                  p                  -                  L                                                                        ]        ∈          C              M        ⁢                  xe2x80x83                ⁢                  (                      L            +            1                    )                xc3x97                  (                      p            +            1                    )                    
where k indicates the sequential position of a received training signal sample in a sequence of received training signal samples and p+1 indicates the number of received training signal samples in each sequence of received training signal samples; defining a matrix S from the sequence of known training symbols as   S  =            [                                                  s              k                                                          s                              k                +                1                                                          …                                              s                              k                +                p                                                                                        s                              k                -                1                                                                        s              k                                            …                                ⋮                                                ⋮                                ⋮                                ⋰                                ⋮                                                              s                              k                -                v                -                L                                                          …                                …                                              s                              k                -                v                -                L                +                p                                                        ]        ∈          C                        xe2x80x83                ⁢                              (                          v              +              L              +              1                        )                    xc3x97          N                    
where v+L+1 is the number of effective channels considered by the equalization processor; initializing hopt to be the first column of a matrix B=(S*P*ST)xe2x88x921S*ST where P=(Ixe2x88x92XH(XXH)xe2x88x921X) and XH is the Hermitian of X; and carrying out iterative steps a predetermined number of times, the iterative steps comprising calculating a vector q=Bhopt and calculating a new value for the vector hopt=q/∥q∥.
An interference detection method is also provided in which a signal-to-interference-plus-noise ratio SINR is determined by: determining orthogonal weights woptxe2x8axa5 of the optimal filter coefficients wopt; determining an interference pulse noise yI from the expression             y      _        I    T    =            ∑              i        =        1                              M          ⁢                      xe2x80x83                    ⁢                      (                          L              +              1                        )                          -        1              ⁢          xe2x80x83        ⁢                            (                                    w              _                                      opt              i                        ⊥                    )                T            ⁢              xe2x80x83            ⁢      X      
where M(L+l)xe2x88x921 is the number of orthogonal weights; determining an estimated desired signal yD from the expression
yDT=(wopt)TX; and
determining the SINR as the ratio of the square of the magnitude of the interference pulse noise to the square of the magnitude of the estimated desired signal.
The methods provide an efficient means for determining the optimal filter coefficients and the optimal effective channel coefficients used by the space-time filter and the equalizer respectively. Furthermore, the accuracy of the sequence estimation is improved.